A Game-Theory View Of Arms Race In Middle East – Analysis

By Dr. Kazem Yavari*

According to the literature of game theory, a game generally consists of three elements: 1. set of players, 2. set of strategies for each player and 3. Set of payoffs. Set of payoffs simply tells us how much each player obtains or lose from a chosen profile of strategies. Game theory can be applied to many economic, social and political situations in the real world. Modelling a political situation within a game is mainly an art and indeed it is very difficult to put all characteristics of players’ behavior into a simple game. Nevertheless, to analyze a political situation in the real world, we need to focus on important aspects of the situation.

There are various games, each with a different structure. To me, the ongoing arms racing in the Middle East region and in particular between Iran and Saudi Arabia is more or less consistent with the structure of the so-called “catching a precious deer” game. Before analyzing this arms racing, it is informative to have a brief look at this game and its payoffs structure. In this game, two individuals try to catch a precious deer together and have agreed to share equally the benefit. Each individual knows that the deer is caught only if both cooperate together. Without cooperation, the deer will simply scape and nobody benefit. However, while the two individuals are getting closer and closer to the deer, they see goats are moving around. So, there is always a fear that one or both of them simply become negligent and get distracted by the goat. Therefore, in this simple game, each individual has two strategies: Watch carefully for the deer (D) or look for goat (G).

According to the literature of game theory, this simple game has two equilibria. By equilibrium, I mean a profile of strategies such that nobody has incentive to deviate from his strategy given his opponent’s strategy. Having this definition in mind, we see that one superior equilibrium is that both individuals watch carefully to catch the deer (D, D). Given that one player chooses “D”, the best strategy for the other player is “D” as well since Deer is better than Goat. The second equilibrium is an inferior equilibrium and this is when both individuals get distracted and follow the goat (G, G). Again, given that one chooses “G”, the best for the other one is “G” as well since Goat is better than nothing.

However, the profiles in which that one individual watches carefully for the deer and the other one looks for the goat [(W, C) or (C, W)] cannot be equilibria of this game since given that one chooses strategy “G”, it not optimal for the other one to choose strategy “D”. Unless there is a mutual cooperation between both individuals, there is no internal guarantee within the structure of the above game that ensures the superior equilibrium will be reached. Individuals may end up with (G, G) profile.

In the real world, a number of political situations can be modeled within the above “Catching a precious deer” game. The so-called nuclear arms racing among the world’s big powers and particularly between US and Russia is an example. There is no doubt that the world will be much safer if both US and Russia disarm themselves. No bomb – No bomb (NB, NB) is the superior equilibrium for the whole world. However, Bomb-Bomb (B, B) is also an equilibrium even though it is inferior and has much lower payoffs or even totally a loss for the entire world. The other profiles, (NB, B) and (B, NB) are not equilibrium. It is not optimal for Russia to disarm itself if US keeps nuclear bomb and vice versa. A similar situation is between India and Pakistan. Global warming is another situation. The world is much safer if everybody cuts greenhouse gases. But, since US refrain from doing that, China, Brazil, India and other big economies are reluctant to cut. So, the world end up with everybody maximizing industrial production, creating a disaster for the entire world.

To me, the ongoing arms racing between Iran and Saudi Arabia can be modelled by a game which has more or less the structure of “catching a precious deer” game. These two countries must understand that they are not involved in a zero-sum game in which one country has to win eventually and the other has to lose. Without going into details of all behavioral characteristics, it seems that Iran and Saudi Arabia are intentionally or unintentionally being pushed into this “catching a precious deer” game.

Apparently, each country can follow one of the two strategies: 1. Further accumulation of arms and arms racing and 2. Significant Push for Economic Growth and Development. Putting into economics tradition, each country must decide whether to have more guns (G) or more butter (B). Eventually, one of the following equilibrium profile of strategies will be chosen: (Guns, Guns) or (Butter, Butter). (Guns, Guns) is an inferior equilibrium and (Butter, Butter) is a superior equilibrium. Indeed, the profile strategies in which Saudi Arabia accumulate more arms and Iran not or vice versa, (Guns, Butter) and (Butter, Guns), will not be equilibrium profiles.

Given that Saudi Arabia will choose to buy more arms and increase its military expenditures, it is not optimal for Iran to be indifferent and pursue its economic development without increasing its defense and military expenditures. Also given that Iran is producing and to some extent importing variety of arms, Saudis will not find it optimal to stop arms racing with Iran. One might argue that Saudi Arabia is importing arms while Iran is mainly producing arms and so the situation is not symmetric.

However, we need to say that it does not matter whether to import arms or produce them domestically as long as resources are being taken away from production of butter toward production of more guns. Scarcity is the core of economics and every dollar a country spend on guns, that dollar is no longer available for the production of butter.

Now the question is that if both (Guns, Guns) and (Butter, Butter) are equilibrium, which one will be more likely to happen in reality. In other words, will Saudi Arabia and Iran keeps accumulating arms in future, being trapped in inferior equilibrium or they may be able to find a way toward a superior equilibrium. To answer this question, we have to look for the various factors that affect the likelihood of each case.

There are a number factors that apparently support the fact that the inferior equilibrium (Guns, Guns) will be likely to be the outcome of the game. These factors are as follows:

1. Economics tells us that production of a good will eventually stop unless it is constantly being consumed by someone. Oranges and apples are consumed daily by individuals and their production will never stop. Guns are consumed only in wars and arms racing. Given the fact that US economy very much depends, among other things, on its capabilities to produce a variety of guns, wars and arms racing around the world are the best for US economy in general and US arms producing companies in particular. Once the twin towers collapsed in 9/11, share prices of all US companies fell sharply in the world stock markets, except share prices of companies producing guns. If the produced arms by US and the other big military powers are not consumed within a decade or so, their arms producing companies get into real problems, creating unemployment. Therefore, these external factors directly and indirectly push for arms racing around the world, particularly in regions in which wealthy countries exist to buy arms. Middle East is the best market for arms racing and the rich Persian Gulf countries such as Iran and Saudi Arabia are prominent among others. The recent US multibillion arms deal with Saudi Arabia is the best evidence. Therefore, existence of such external forces and the benefits they obtain from arms racing push both Iran and Saudi Arabia into the inferior equilibrium (Guns, Guns), lowering the chance or likelihood of reaching the superior equilibrium (Butter, Butter).

2. The role of oil in fueling arms racing in the region cannot be ignored. As a result of US military presence in the region and the resulting crises, oil prices sharply increased during the first term of Ahmadinejad. This oil price rise brought an unprecedented oil windfall for the oil exporting countries in the region. In our case, it is said that Ahmadinejad government had more 700 billion dollars in oil revenue. The figure for Saudi Arabia has been much higher. Other countries in the region benefited proportionately from this hike in oil price. What matters for the US government is the total wealth accumulated in the hands of these governments. Now, the US sees that wealth, while its economy is suffering from economic crisis in 2008 and afterward. The only way to recapture that money is through arms racing and destruction of countries in the region. In game theory terminology, the best way for US to recapture that money is through pushing players in the region into a burning inferior equilibrium which is arms racing.

3. Ethnic, Religion and language differences between Iran and Saudi Arabia as well as their historical low trust make the superior equilibrium less likely to be reached. Although manifestation of these differences had faded away to some extent in some periods, particularly at the time of deceased president Rafsanjani and President Khatami, they flourished again during the President Ahmadinejad, lowering economic and political cooperation between the two countries and the likelihood of superior equilibrium.

4. Acts of pressure groups and hardliners in both countries have been always in favor of inferior equilibrium. In Saudi Arabia, Wahhabis’ pressure on Iranians during Haj Time and presence of more anti-Shiite groups within the government get feedbacks inside Iran. In Iran, attack on Saudi Embassy in Tehran, created many problems for Iranian foreign ministry and the immediate Saudis feedback was to cut all diplomatic relations. Although these wounds on both sides may get healed over time, they lower the chance of economic and political cooperation for the purpose of development of both countries.

5. The unresolved situations in Yemen, Syria, and Iraq and involvement of Iran and Saudi Arabia in these countries in one way or the other, created an unprecedented distance between the two countries. Indeed, one of the main reason for Saudis to boost their military expenditures and arms importation from US is their military involvement in Yemen and to some extent indirectly in Syria and Iraq. The real problem is the huge differences in their preferences which distance them to a maximum extent from each other, giving support to the increasing chance of inferior equilibrium for the two countries.

However, we should not be totally pessimistic about future cooperation between Iran and Saudi Arabia. We hope that the two countries reach a superior equilibrium in a foreseeable future, helping the entire Muslim World to enjoy the fruits of economic development and prosperity. Some of the factors that might help the two countries to reach the superior equilibrium are as follow:

1. Re-election of Dr. Hassan Rouhani might change the trajectory of Iran’s movement in the region as it did so in the world arena when he could reach a historic nuclear agreement with 5+1 more than a year ago. His repeated campaign promise that Iran wants to create a bridge to the world economy and cooperate with almost all countries on economic and political grounds, indicate that Iranian government is serious on the issue of cooperation.

2. Haj and Omrah are two important ceremonies that may help Iran and Saudi Arabia not to lose their hope totally in reaching a superior equilibrium in future. Keeping these ceremonies is vital for both of them.

3. In addition to its ambition for arms racing, Saudi Arabia desires to unite its neighbors against Iran. Fortunately, the recent reluctance from Qatari government created a doubt on Saudis ability to isolate Iran. If further differences are created and we observe more gaps among the Arab countries in this regard, the benefit of the inferior equilibrium of arms racing for Saudi Arabia will decline over time.

4. On the Iran side, a solid bridge with the west lowers the benefits of arms racing. Gradual removal of sanctions and increasing foreign investment in Iran makes Saudi Arabia more isolated and they may start thinking about cooperation rather than racing with Iran.

5. The last but not the least is a unilateral signal and movement from either side of the game. Although this is very difficult and each one is not willing at the moment to do so, ignition of a friendly act is like creating a small hole in dark room, searching for light. That light may eventually guide both countries toward a magnificent platform. This is what the entire Muslim world expect from these two important countries in the region.

In summary, in addition to a superior equilibrium, the game of “catching a precious deer” has unfortunately an inferior equilibrium in which both players lose or earn nothing in the long term. Cooperation is much safer and better than arms racing. Iran and Saudi Arabia must firstly understand that they are not playing a zero-sum game, but a positive-sum game. Both can get maximum benefits if they wisely can find a way toward the illuminating superior equilibrium and start distancing gradually themselves from the destructing inferior equilibrium by which they earn very little and the Trump’s government gets a bonanza.

* Dr. Kazem Yavari
Associate Professor of Economics
Tarbiat Modares University

**These views represent those of the author and are not necessarily Iran Review’s viewpoints.


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Iran Review is a Tehran-based site that is independent, non-governmental and non-partisan and representing scientific and professional approaches towards Iran’s political, economic, social, religious, and cultural affairs, its foreign policy, and regional and international issues within the framework of analysis and articles.

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